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The cylindrical coordinate robot on a factory's assembly line is shown in a top view. The 65 N force acts on a workpiece being held at the end of the robot's arm. Express the 65 N force as a vector in terms of unit vectors i and j that are aligned with the z- and y-axes. y 70° 30° Express your answer as a vector using the unit vectors i and j. (Express your answer using three significant figures.) F jN

The cylindrical coordinate robot on a factory's assembly line is shown in a top view. The 65 N force acts on a workpiece being held at the end of the robot's arm. Express the 65 N force as a vector in terms of unit vectors i and j that are aligned with the z- and y-axes. y 70° 30° Express your answer as a vector using the unit vectors i and j. (Express your answer using three significant figures.) F jN

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The cylindrical coordinate robot on a factory's assembly line is shown in a top view. A force of 65 N acts on a workpiece being held at the end of the robot's arm. The goal is to express the 65 N force as a vector in terms of unit vectors \( \mathbf{i} \) and \( \mathbf{j} \), which are aligned with the \( x \)- and \( y \)-axes. ### Diagram Explanation In the diagram: - The robot arm is positioned at a 30° angle from the positive x-axis. - The force vector \( \mathbf{F} \) is applied at a 70° angle from the robot arm. ### Vector Representation To express the force vector \( \mathbf{F} \) using \( \mathbf{i} \) and \( \mathbf{j} \), it requires resolving the force into its x and y components: - The x-component (\( F_x \)) of the force can be calculated with: \[ F_x = 65 \cos(30° + 70°) \] - The y-component (\( F_y \)) of the force can be calculated with: \[ F_y = 65 \sin(30° + 70°) \] ### Expression Express your answer as a vector using the unit vectors \( \mathbf{i} \) and \( \mathbf{j} \). \[ F = \underline{\hspace{1cm}} \mathbf{i} + \underline{\hspace{1cm}} \mathbf{j} \text{ N} \] (Make sure to express your answer using three significant figures.)
Transcribed Image Text:The cylindrical coordinate robot on a factory's assembly line is shown in a top view. A force of 65 N acts on a workpiece being held at the end of the robot's arm. The goal is to express the 65 N force as a vector in terms of unit vectors \( \mathbf{i} \) and \( \mathbf{j} \), which are aligned with the \( x \)- and \( y \)-axes. ### Diagram Explanation In the diagram: - The robot arm is positioned at a 30° angle from the positive x-axis. - The force vector \( \mathbf{F} \) is applied at a 70° angle from the robot arm. ### Vector Representation To express the force vector \( \mathbf{F} \) using \( \mathbf{i} \) and \( \mathbf{j} \), it requires resolving the force into its x and y components: - The x-component (\( F_x \)) of the force can be calculated with: \[ F_x = 65 \cos(30° + 70°) \] - The y-component (\( F_y \)) of the force can be calculated with: \[ F_y = 65 \sin(30° + 70°) \] ### Expression Express your answer as a vector using the unit vectors \( \mathbf{i} \) and \( \mathbf{j} \). \[ F = \underline{\hspace{1cm}} \mathbf{i} + \underline{\hspace{1cm}} \mathbf{j} \text{ N} \] (Make sure to express your answer using three significant figures.)
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